On tail behaviour of stationary second-order Galton-Watson processes with immigration
Abstract
A second-order Galton-Watson process with immigration can be represented as a coordinate process of a 2-type Galton-Watson process with immigration. Sufficient conditions are derived on the offspring and immigration distributions of a second-order Galton-Watson process with immigration under which the corresponding 2-type Galton-Watson process with immigration has a unique stationary distribution such that its common marginals are regularly varying. In the course of the proof sufficient conditions are given under which the distribution of a second-order Galton-Watson process (without immigration) at any fixed time is regularly varying provided that the initial sizes of the population are independent and regularly varying.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2018
- DOI:
- 10.48550/arXiv.1801.07931
- arXiv:
- arXiv:1801.07931
- Bibcode:
- 2018arXiv180107931B
- Keywords:
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- Mathematics - Probability;
- 60J80;
- 60G70
- E-Print:
- 43 pages. arXiv admin note: text overlap with arXiv:1805.00820